Solve for $x$ and $y$ using elimination. ${3x-2y = 22}$ ${x+3y = 22}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the bottom equation by $-3$ ${3x-2y = 22}$ $-3x-9y = -66$ Add the top and bottom equations together. $-11y = -44$ $\dfrac{-11y}{{-11}} = \dfrac{-44}{{-11}}$ ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $\thinspace {3x-2y = 22}\thinspace$ to find $x$ ${3x - 2}{(4)}{= 22}$ $3x-8 = 22$ $3x-8{+8} = 22{+8}$ $3x = 30$ $\dfrac{3x}{{3}} = \dfrac{30}{{3}}$ ${x = 10}$ You can also plug ${y = 4}$ into $\thinspace {x+3y = 22}\thinspace$ and get the same answer for $x$ : ${x + 3}{(4)}{= 22}$ ${x = 10}$